Timeline for Moduli of extensions of modules
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24, 2010 at 15:50 | comment | added | Mariano Suárez-Álvarez | @Daniel, that really depends on the starting data. For example, if the algebra $A$ is the group algebra of a finite group (over a field of characteristic zero) you do get a (zero-dimensional) scheme. | |
| May 24, 2010 at 15:26 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
added 132 characters in body
|
| May 22, 2010 at 14:18 | comment | added | Daniel Larsson | I can almost guarantee that a scheme structure does NOT exist on such a quotient. In fact, unless I misunderstood something, this is more or less equivalent to the problem of describing a moduli space of $n\times n$-matrices up to conjugacy. And this can never exist as a moduli space, even in a coarse sense. See the paper by Mumford and Suominen "An introduction to the theory of moduli", 1970. | |
| May 22, 2010 at 9:42 | comment | added | Heinrich Hartmann | Thanks for your answer. Your hint for the first point is really helpful. Ad II) I have seen people (e.g. Reineke arXiv:0802.2147) doing the moduli of quiver representations using a similar construction and GIT quotients. So I am confident that one can produce a sheme in the way you described. However, the application I have in mind goes as follows. Suppose $E_i$ are sheaves on an algebraic variety and $E_i$ are stable in some stability cndition. How many sheaves $E$ have a Hader-Narasimhan filtration with semi-stable factors $E_i$? In this case Artin-Algebras are only of limited help. | |
| May 22, 2010 at 5:35 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 2.5 |